125 LearnersLast updated on May 26th, 2025
Square Root of 751
If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in many fields such as vehicle design, finance, etc. Here, we will discuss the square root of 751.
What is the Square Root of 751?
The square root is the inverse operation of squaring a number. 751 is not a perfect square. The square root of 751 is expressed in both radical and exponential form. In radical form, it is expressed as √751, whereas in exponential form it is expressed as (751)^(1/2). √751 ≈ 27.4014, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 751
The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 751 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 751 is broken down into its prime factors.
Step 1: Finding the prime factors of 751 Breaking it down, we find that 751 is itself a prime number.
Step 2: Since 751 is not a perfect square and is a prime number, we cannot group any digits into pairs.
Therefore, calculating the square root of 751 using the prime factorization method is not possible.
Square Root of 751 by Long Division Method
The long division method is particularly used for non-perfect square numbers. In this method, we find the closest perfect square numbers for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin, group the numbers from right to left. For 751, we group it as 51 and 7.
Step 2: Find n whose square is less than or equal to 7. We can use n = 2 because 2^2 = 4 is less than 7. The quotient is 2, and after subtracting, the remainder is 3.
Step 3: Bring down 51, making the new dividend 351. Add the old divisor (2) to the same number to get 4, which becomes our new divisor.
Step 4: The new divisor is 4n. Find n such that 4n × n is less than or equal to 351. Let n = 7, then 47 × 7 = 329.
Step 5: Subtract 329 from 351; the difference is 22, and the quotient is 27.
Step 6: Since the dividend is less than the divisor, add a decimal point and two zeroes to the dividend, making it 2200.
Step 7: Find the new divisor, which is 27 (since 274 × 8 = 2192).
Step 8: Subtract 2192 from 2200, giving a remainder of 8.
Step 9: The quotient is now 27.4.
Step 10: Continue these steps until you achieve the desired precision.
So the square root of √751 ≈ 27.4014.
Square Root of 751 by Approximation Method
The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let's learn how to find the square root of 751 using this method.
Step 1: Find the closest perfect squares to √751.
The smallest perfect square less than 751 is 729, and the largest perfect square above 751 is 784. √751 falls between 27 and 28.
Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (751 - 729) / (784 - 729) = 22 / 55 ≈ 0.4 Add this to the smaller square root: 27 + 0.4 = 27.4
Thus, the square root of 751 is approximately 27.4014.
Common Mistakes and How to Avoid Them in the Square Root of 751
Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at a few common mistakes in detail.
Mistake 1
Forgetting about the negative square root
Students should be aware that a number has both positive and negative square roots. However, usually, only the principal (positive) square root is used for practical purposes. For example, √50 = 7.07, but there is also -7.07.
Mistake 2
Not adding the square root symbol in proper places
Misusing the square root symbol is another common error. Students should simplify numbers inside the square root first before further calculations.
For example, √(12+24) = √36, not √12 + √24.
Mistake 3
Not finding the correct value of a non-perfect square
Students should simplify numbers inside the square root to avoid errors in identifying approximate values.
For example, √50 ≈ 7.071, not 7.
Mistake 4
Confusing the square root symbol with the cube root
Students need to distinguish between cube root and square root symbols.
For example, √50 and ∛50 are different.
Mistake 5
Making mistakes in long division
The long division method involves many steps, and students may skip a step accidentally, leading to incorrect results. This may occur in subtraction or elsewhere.
Square Root of 751 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √751?
The area of the square is approximately 751 square units.
Explanation
The area of the square = side^2.
The side length is given as √751.
Area of the square = side^2 = √751 × √751 = 751 square units.
Therefore, the area of the square is approximately 751 square units.
Problem 2
A square-shaped building measuring 751 square feet is built; if each of the sides is √751, what will be the square feet of half of the building?
375.5 square feet
Explanation
We can divide the given area by 2 since the building is square-shaped.
Dividing 751 by 2 gives us 375.5.
So half of the building measures 375.5 square feet.
Problem 3
Calculate √751 × 5.
137.007
Explanation
First, find the square root of 751, which is approximately 27.4014.
Then, multiply 27.4014 by 5.
So, 27.4014 × 5 ≈ 137.007.
Problem 4
What will be the square root of (751 + 9)?
The square root is 29.
Explanation
To find the square root, first find the sum of (751 + 9). 751 + 9 = 760, and the square root of 760 ≈ 29.
Therefore, the square root of (751 + 9) is approximately ±29.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √751 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is approximately 154.8028 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√751 + 50) = 2 × (27.4014 + 50) ≈ 2 × 77.4014 ≈ 154.8028 units.
FAQ on Square Root of 751
1.What is √751 in its simplest form?
2.What are the factors of 751?
3.Calculate the square of 751.
4.Is 751 a prime number?
5.751 is divisible by?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 751?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 751?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 751
- Square root: A square root is the inverse operation of squaring a number. For example, 4^2 = 16, and the inverse is the square root: √16 = 4.
- Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers (p/q, where q ≠ 0).
- Principal square root: The principal square root is the non-negative square root of a number.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- Decimal: A decimal number is a number that consists of a whole number and a fractional part separated by a decimal point, such as 7.86.
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About BrightChamps in Bahrain
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
